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Here, we develop a matrix reordering algorithm based on graph partitioning techniques that yields the optimal block-tridiagonal form for quantum transport.
We present PQR sort, a matrix reordering algorithm based on a recent data structure called PQR tree, and compare it with the previous ones in terms of time complexity and quality of reordering, according to predefined evaluation criteria.
Therefore, a matrix reordering algorithm is directly related to this concept.
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Matrix reordering algorithms, such as 2D sort and Sugiyama-based reordering, permute matrix rows and columns in order to highlight hidden patterns.
A reordering algorithm of the vertices based on Gibbs method is also introduced.
Reordering algorithms and metrics: Many algorithms can be applied to matrix reordering.
Comparison of other reordering algorithms based on a broad set of metrics is under execution.
This section compares the PQR sort to other approaches for matrix reordering.
Liiv [6] presents a historical overview of some matrix reordering methods.
The matrix reordered by Sugiyama (Figure 9c) seems to reveal three groups of 1-cells, which in this case, may be related to three distinct subjects.
In essence, we are hoping that the algorithm will find the structure that has been buried in Figure 2. In Figure 3 we display the two adjacency matrices reordered with the algorithm; we show reordering with eight different columns of X - T, four from each end of the spectrum.
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